An effective interaction spontaneously arising in a renormalizable model of quantum field theory

TL;DR

This paper investigates how a massless scalar field with a cubic interaction in six dimensions can spontaneously develop an effective quartic interaction, indicating a potential scale invariance breaking in a renormalizable quantum field theory.

Contribution

It demonstrates the spontaneous emergence of an effective $\,\phi^4$ interaction from a $\,g \phi^3$ model using Bogolubov quasi-averages, revealing a non-trivial solution and parameter relations.

Findings

Non-trivial solution for the form-factor exists.

Relations between interaction parameters are established.

The non-trivial solution is argued to be stable.

Abstract

Theory of massless scalar field $\phi$ with interaction $g \phi^3$ in six-dimensional space is considered. A possibility of initial scale invariance breaking, which results in a spontaneous arising of effective interaction $G \phi^4$, is studied by application of Bogolubov quasi-averages approach. It is shown, that compensation equation for form-factor of this interaction in approximation up to the third order in $G$ has a non-trivial solution. The conditions imposed on form-factor value at zero and scalar field mass $m$ fix the unique solution, which gives relations between parameters of interaction $g \phi^3$ and parameters $G $ and $m$. Arguments are laid down in favour of a stability of the non-trivial solution.